Using archival X-ray observations and a log-normal population model, we estimate constraints on the intrinsic scatter in halo mass at fixed optical richness for a galaxy cluster sample identified in Dark Energy Survey Year-One (DES-Y1) data with the redMaPPer algorithm. We examine the scaling behavior of X-ray temperatures, TX, with optical richness, λRM, for clusters in the redshift range 0.2 < z < 0.7. X-ray temperatures are obtained from Chandra and XMM observations for 58 and 110 redMaPPer systems, respectively. Despite non-uniform sky coverage, the TX measurements are >50% complete for clusters with λRM > 130. Regression analysis on the two samples produces consistent posterior scaling parameters, from which we derive a combined constraint on the residual scatter, σln T | λ = 0.275 ± 0.019. Joined with constraints for TX scaling with halo mass from the Weighing the Giants program and richness–temperature covariance estimates from the LoCuSS sample, we derive the richness-conditioned scatter in mass, σln M | λ = 0.30 ± 0.04 (stat) ± 0.09 (sys),, at an optical richness of approximately 100. Uncertainties in external parameters, particularly the slope and variance of the TX–mass relation and the covariance of TX and λRM at fixed mass, dominate the systematic error. The 95% confidence region from joint sample analysis is relatively broad, σln M | λ ∈ [0.14, 0.55], or a factor ten in variance.